Translating Words to Expressions

Translating Words to Expressions

• Key Terms and Their Representations:

  • Sum: Addition (e.g., "more than," "increased by")
    • Expression: a + b
  • Difference: Subtraction (e.g., "less than," "decreased by")
    • Expression: a - b
  • Product: Multiplication (e.g., "times," "of")
    • Expression: a × b or ab
  • Quotient: Division (e.g., "divided by," "per")
    • Expression: a ÷ b or a/b

• Common Phrasing:

  • "The sum of a and b" → a + b
  • "The difference between a and b" → a - b
  • "Three times a number (x)" → 3x
  • "A number decreased by ten" → x - 10
  • "Half of a number (x)" → x/2 or 0.5x

• Translating Word Problems:

  1. Identify Keywords: Look for terms indicating operations (addition, subtraction, etc.).
  2. Define Variables: Assign letters to unknown quantities (e.g., let x = the unknown number).
  3. Create Expressions: Combine keywords and variables to form a mathematical expression.
  4. Check for Clarity: Ensure the expression accurately represents the scenario described.

• Examples:

  • "A number increased by 5" → x + 5
  • "The product of 7 and a number (y)" → 7y
  • "Twice a number decreased by 4" → 2x - 4

• Practice Tips:

  • Convert various word problems to expressions to enhance understanding.
  • Familiarize yourself with synonyms for keywords to broaden expression formation skills.
  • Review common phrases and practice translating them into mathematical symbols.

Translating Words to Expressions

• Key Terms and Their Representations:

  • Sum: Represents addition; indicated by phrases such as "more than" or "increased by."
    • Mathematical Expression: a + b
  • Difference: Represents subtraction; expressed with terms like "less than" or "decreased by."
    • Mathematical Expression: a - b
  • Product: Indicates multiplication; expressed through words like "times" or "of."
    • Mathematical Expression: a × b or ab
  • Quotient: Represents division; shown with terms such as "divided by" or "per."
    • Mathematical Expression: a ÷ b or a/b

• Common Phrasing:

  • "The sum of a and b" directly translates to a + b.
  • "The difference between a and b" can be represented as a - b.
  • "Three times a number (x)" is expressed mathematically as 3x.
  • "A number decreased by ten" translates to x - 10.
  • "Half of a number (x)" translates to x/2 or 0.5x.

• Translating Word Problems:

  • Identify Keywords: Look for specific terms indicating mathematical operations.
  • Define Variables: Assign variables (e.g., let x = the unknown number) to unknown quantities.
  • Create Expressions: Combine identified keywords and defined variables to form mathematical expressions.
  • Check for Clarity: Ensure that the expression accurately reflects the scenario presented.
    • Examples:
      • "A number increased by 5" translates to x + 5.
      • "The product of 7 and a number (y)" translates to 7y.
      • "Twice a number decreased by 4" can be expressed as 2x - 4.

• Practice Tips:

  • Regularly convert word problems into expressions to improve comprehension.
  • Familiarize with synonyms for keywords to enhance expression formation abilities.
  • Review and practice common phrases to translate them into mathematical symbols effectively.

Test your skills in converting verbal phrases into mathematical expressions. This quiz will guide you through key terms, common phrasings, and tips for translating word problems into algebraic formats. Perfect for students learning how to interpret and solve word problems.